The theory of Inflation explains the apparent consistency of the universe by proposing that the early universe grew exponentially for a 1E-36 seconds. Isn't a simpler explanation that the universe is just older and so the homogeneousness comes from a slower more steady growth? Is there any evidence that rules out a slow growing universe and supports Inflation theory?

The question seems to be more about observation, not theory, but the biggest problems with inflation are theoretical. Paul Steinhardt has a pretty cogent critique. See Paul Steinhardt, "The Inflation Debate," Sci Am, Apr 2011, p. 38, and pirsa.org/11070029 , notes here physicsforums.com/showthread.php?p=3404021#post3404021 . Basically the critique is that inflation rewards procrastinating "rogue" regions that don't stop inflating, and this leads to a lack of predictive power. Arguably inflation requires more fine-tuning than no inflation (i.e., its probability is lower).
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Ben CrowellAug 11 '11 at 14:45

5 Answers
5

I can not go into much detail here but let me say that exponential growth brings many things that we see around us right now: absence of magnetic monopoles, a homogeneous universe in which no section is a "preferred" section i.e. has more matter density, and many more observable quantities.

And it should also be mentioned that while the universe is quite homogenous globally it also contains local inhomogeneities that can't very well be explained otherwise than by an enormous expansion of quantum fluctuations in the early universe. And the observed data actually matches the inflation calculations.
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MarekNov 17 '10 at 23:56

As pointed out by Weinberg in his book Cosmology (note, this is NOT Gravitation and Cosmology. He also has a book of that name), inflation was proposed to explain 3 problems:
1)Horizon problem
2)Flatness problem
3)Monopole problem

1)Horizon problem: The evolution of the scale factor before and after decoupling is $\sqrt{t}$ and $t^{\frac{2}{3}}$. We compute the linear dimension of the forward and backward lightcones at the time of decoupling in the hot big bang model. The radius of this light cone is the physical size of the region on the last scattering surface from which we receive the CMB. The backward lightcone is $l_{B} \approx 3(t_{dec}^{2}t_{0})^{1/3}$ ($t_{0}$ is present time.). The forward lightcone radius is $l_{F} = 2t_{dec}$. The ratio $R \equiv \frac{l_{B}}{l_{F}} \approx 70$. The physical wavelength associated with cosmological perturbations grows faster than the Hubble radius as we go back in time. If, a causal mechanism is responsible for the inhomogenities, then these scales should be inside Hubble scale in very early universe. This is possible if, the perturbation associated wavelength decreases faster than Hubble radius as we go back in time. So, $-\frac{d}{dt}\left( \frac{\lambda}{d_{H}}\right) <0 $ ($d_{H}$ is the Hubble radius). This leads to $\ddot{a} >0$. In most cases, we model it as a single scalar field which causes this inflation in a de Sitter background ($\Lambda$ dominated universe)

2)Flatness problem: A less convincing argument of inflation. Experimentally, we observe a vanishing spatial curvature parameter $\Omega_{K} = -\frac{K}{a^2 H^2} = -\frac{K}{a^2}$. In solving this problem, we assume that nothing much happens to the cosmic scale factor and expansion rate from the end of inflation to the beginning of the radiation dominated era i.e $a_{Inflation}H_{Inflation} \approx a_{rad. domination}H_{rad. domination}$. The small value of $|K|/\dot{a}^2$ could be explained by taking $K=0$ i.e a spatially flat universe. However, inflation opens up the possibility that the universe is not at all homogenous and isotropic and that its apparent flatness of the cosmic metric is just the result of inflation.

3)Monopole problem: Standard Model predicts that in a hot early universe, a large number of monopoles must be produced by symmetry breaking from some single gauge theory since it is at an energy scale of about $M = 10^{16}$ GeV. Those monopoles should have persisted even to the present days. However, that is not the case.

Amongst all the above problems, the horizon problem is the most serious one. Since, the other two can be explained by other mechanisms. Also, any number of $e$-foldings not only solves the horizon problem but also the flatness problem and the monopole problem.

I was about to take out my copy of Weinburg to help craft my answer :P
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Benjamin HorowitzAug 11 '11 at 18:06

"Standard Model predicts that in a hot early universe, a large number of monopoles must be produced by symmetry breaking from some single gauge theory[...]" Huh? The standard model doesn't have monopoles, does it?
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Ben CrowellJul 26 '13 at 4:25

The main (and original) reason for the proposal of inflationary theory was the horizon problem. That is, the fact the the universe is so incredibly homogeneous and isotropic despite the fact that some parts of the universe are apparently too far away to have exchanged energy. Inflation in the early universe is a powerful explanation for this intriguing observation. Also of note is the flatness problem, which inflation also helps address.

There are of course various other theories to explaining this problems, not in any way related to inflation, such as the varying speed of light (VSL) theory. These are however under active research and still not widely accepted.

Personally I think the standard arguments are not yet conclusive. The horizon problem, or the homogeneity problem, can be explained by assuming that the initial condition is homogeneous, without assuming that causal contact in the early universe has smoothed out inhomogeneities. You may object that a homogeneous initial condition is "unnatural", but since we know so little about the big bang singularity, there's nothing conclusive that can be said. The monopole problem is only a problem if you think monopoles exist, which has no empirical evidence so far. The curvature problem, again, is a "naturalness" problem, but we lack a precise definition of naturalness given our inability to understand the big bang singularity.

Abstract
...We discuss these findings in relation to expectation
from standard inflationary cosmology ...
Summary
The study of alignments in the low ℓ CMB has found a
number of peculiarities. We have shown that the alignment of the
quadrupole and octopole planes is inconsistent with Gaussian,
statistically isotropic skies at least at the 99% confidence
level. Further a, number of (possibly related) alignments occur at
95% confidence levels or greater. Putting together these provides
a strong indication that the full-sky CMB WMAP maps are inconsistent
with the standard cosmological model at the large-angles. Even
more peculiar is the alignment of the quadrupole and octopole with
solar system features (the ecliptic plane and the dipole).

Introduction
In this regard, it is worth noting that our record at
predicting the gross properties of the universe on large scales from
first principles has been rather poor. According to the standard
concordance model of cosmology, over 95% of the energy content of the
universe is extraordinary—dark matter or dark energy whose existence
has been inferred from the failure of the Standard Model of particle
physics plus General Relativity to describe the behavior of
astrophysical systems larger than a stellar cluster—while the very
homogeneity and isotropy (and inhomogeneity) of the universe owe to
the influence of an inflaton field whose particle-physics-identity is
completely mysterious even after three decades of theorizing.

Conclusions ... The CMB is widely regarded as offering strong
substantiating evidence for the concordance model of cosmology. Indeed
the agreement between theory and data is remarkable—the patterns in
the two-point correlation functions (TT, TE, and EE) of Doppler peaks
and troughs are reproduced in detail by fitting with only six (or so)
cosmological parameters. This agreement should not be taken lightly;
it shows our precise understanding of the causal physics on the last
scattering surface. Even so, the cosmological model we arrive at is
baroque, requiring the introduction at different scales and epochs of
three sources of energy density that are only detected
gravitationally—dark matter, dark energy and the inflaton. This
alone should encourage us to continuously challenge the model and
probe the observations particularly on scales larger than the horizon
at the time of last scattering.

At the very least, probes of the large-angle (low-ℓ) properties of the
CMB reveal that we do not live in a typical realization of the
concordance model of inflationary ΛCDM.

Cold dark matter, which is an important means of testing inﬂation, is
a ten-parameter theory, $h,\Omega_Bh^2,S,n,dn/d \ln{k}, T/S, nT,
> \Omega_\nu,g_*, \Omega_\Lambda$ . While this is a daunting number of
parameters, especially for a cosmological theory, there is good
reason to believe that within ten years the data will
overdetermine these parameters. Crucial to achieving this goal are the
high-precision, high-resolution measurements of CBR anisotropy that
will be made over the next decade by...
...ΛCDM is consistent with all the observations discussed here as well as others;...
...Inﬂation Makes Three Robust Predictions
1 Flat universe
2 Nearly scale-invariant spectrum of gaussian density perturbations
3 Nearly scale-invariant spectrum of gravitational waves

Thank you for the references. But, it should be noted that neither of the first two papers criticising inflation was published in a leading journal, so it might not represent scientific consensus.
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mtrencseniAug 10 '11 at 15:11

@mtrencseni the first link is a regular peer-review publisher. Beeing open-access is not the same as low quality.Some papers, even from large affiliated teams, that deal with inconvenient data had been published in obscure locations; I wonder why: I envision similar problems to peer-review of climate research. Dark interests may be hiding behind the scene. The other paper (about a 'scaling universe') is unpublishable because it is against mainstream beliefs (consensus), but it is also mainstream as old as Newton and Coulomb laws are, and the argument is so simple that you can understand it.
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Helder VelezAug 10 '11 at 16:25

1

I didn't say it's not peer-reviewed, I said it's not a leading journal.
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mtrencseniAug 10 '11 at 16:34

The vixra paper is pure crackpottery. The other two papers do not support your statement that "the evidence is against."
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Ben CrowellAug 10 '11 at 17:02

@Crowell Then in your oppinion what are the possible interpretations of: a strong indication that the full-sky CMB WMAP maps are inconsistent with the standard cosmological model ?
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Helder VelezAug 10 '11 at 18:27